Introduction to Stochastic Processes Mathematics & Economics Essay

Introduction to Stochastic Processes
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Markov summarized his findings on the patterns of vowels and consonants in 20,000 Russian letters of the alphabet from Alexander Pushkin’s novel Eugene Onegin focusing the first chapter and sixteen stanzas of the second (Markov, 1913/ 2006). Statistical analysis of the literary text led to the development of the Markov chain theory.Markov first begins by considering 20,000 connected trials that are vowels or consonants and assumes the existence of an unknown constant probability. He then sought to get the approximate value of p through observations where the vowels and consonants were counted. Markov determined the probability of a letter being a vowel or a consonant from a combination of letters
The approximation of the probability is based on the idea that the probability of all the elements is 1, so if the probability of vowels is p0, the probability of constants is q0 or 1-p0. The se...